1 | Verification that the generic case has one solution
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2 | ----------------------------------------------------------------
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3 | (C1) eqns:[ (2) * U1 + ( - X2 - X3), (2) * V1 + ( - Y3), (2) * U2 + ( - X3), (2) * V2 + ( - Y3), (2) * U3 + ( - X2), (2) * V3, ( - 3 * X2 * Y3) * Y + (X2 * Y3^2), ( - 3 * X2 * Y3^2) * X + (X2^2 * Y3^2 + X2 * X3 * Y3^2) ];
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4 |
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5 | (D1) [- X3 - X2 + 2 U1, 2 V1 - Y3, 2 U2 - X3, 2 V2 - Y3, 2 U3 - X2, 2 V3,
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6 |
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7 | 2 2 2 2 2
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8 | X2 Y3 - 3 X2 Y Y3, X2 X3 Y3 + X2 Y3 - 3 X X2 Y3 ]
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9 | (C2) solve(%,[x,y,u1,v1,u2,v2,u3,v3]);
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10 |
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11 | X3 + X2 Y3 X3 + X2 Y3 X3 Y3 X2
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12 | (D2) [[X = -------, Y = --, U1 = -------, V1 = --, U2 = --, V2 = --, U3 = --,
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13 | 3 3 2 2 2 2 2
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14 |
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15 | ----------------------------------------------------------------
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16 | >(load "midpoints")
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17 | Loading midpoints.lisp
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18 | Condition:
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19 | Green list: [ ]
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20 | Red list: [ X2 * Y3^2 ]
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21 | Basis: [ (2) * U1 + ( - X2 - X3), (2) * V1 + ( - Y3), (2) * U2 + ( - X3), (2) * V2 + ( - Y3), (2) * U3 + ( - X2), (2) * V3, ( - 3 * X2 * Y3) * Y + (X2 * Y3^2), ( - 3 * X2 * Y3^2) * X + (X2^2 * Y3^2 + X2 * X3 * Y3^2) ]
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22 | Condition:
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23 | Green list: [ X2 ]
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24 | Red list: [ Y3 ]
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25 | Basis: [ (2) * U1 + ( - X3), (2) * V1 + ( - Y3), (2) * U2 + ( - X3), (2) * V2 + ( - Y3), (2) * U3, (2) * V3, ( - Y3) * X + (X3) * Y ]
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26 | Condition:
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27 | Green list: [ Y3 ]
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28 | Red list: [ X2 + X3 ]
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29 | Basis: [ (2) * U1 + ( - X2 - X3), (2) * V1, (2) * U2 + ( - X3), (2) * V2, (2) * U3 + ( - X2), (2) * V3, (X2 + X3) * Y ]
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30 | Condition:
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31 | Green list: [ Y3, X2 + X3 ]
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32 | Red list: [ X3 ]
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33 | Basis: [ (2) * U1, (2) * V1, (2) * U2 + ( - X3), (2) * V2, (2) * U3 + (X3), (2) * V3, (3 * X3) * Y ]
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34 | Condition:
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35 | Green list: [ X2, Y3, X3 ]
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36 | Red list: [ ]
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37 | Basis: [ (2) * U1, (2) * V1, (2) * U2, (2) * V2, (2) * U3, (2) * V3 ]
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38 | Finished loading midpoints.lisp
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39 | T
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40 |
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